1. What is Square Root?

The square root of a number x is a value y that, when multiplied by itself, gives the original number x. It is a fundamental mathematical operation used in various fields including geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the square root formula:

Where:

• \( x \) — Input value (must be non-negative)
• \( y \) — Square root result

Explanation: The calculator computes the principal square root of the given non-negative number using PHP's built-in sqrt() function.

3. Importance of Square Root Calculation

Details: Square root calculations are essential in various mathematical and scientific applications, including distance calculations, quadratic equations, statistical analysis, and geometric computations.

4. Using the Calculator

Tips: Enter a non-negative number in the value field. The calculator will compute and display the square root. Negative numbers are not allowed as they produce complex results.

5. Frequently Asked Questions (FAQ)

Q1: Why can't I input negative numbers?
A: The square root of a negative number is a complex number (involving imaginary unit i), which this calculator does not handle as it focuses on real number results.

Q2: How precise are the results?
A: Results are calculated with high precision (up to 6 decimal places) using PHP's built-in mathematical functions.

Q3: What is the square root of zero?
A: The square root of zero is zero, as 0 × 0 = 0.

Q4: Can I calculate square roots of very large numbers?
A: Yes, the calculator can handle very large numbers within PHP's floating-point number limits.

Q5: Are there alternative methods to calculate square roots?
A: Yes, methods include the Babylonian method, Newton's method, and using logarithms, but this calculator uses the optimized built-in sqrt() function for accuracy and efficiency.